McDonald's has finally listened to every hung-over wretch who has ever run into a unit at 11:01 a.m., just in time to see the menus roll over and all those delightful Egg McMuffins disappear behind a wall of lunch food. The chain says it's considering rolling out an all-day breakfast, and possibly even delivery.

When asked if all-day breakfasts could be in the cards for McDonald's, president and chief executive Don Thompson told CNBC that it was an option.

"Yes, we would consider it," he said. "We have the focus on our existing menu, but we have looked at breakfast across the day. We have it in some markets around the world."

Thompson also mentioned that the chain had looked at "innovative ways" of extending the breakfast hours, so while a full all-day breakfast might not be coming soon, breakfast might at least be getting a bigger window.

"I think we'll be seeing some of those things in the near future," he said.

McDonald's already offers delivery in some countries, and the company is considering bringing it to more places in the U.S.

"Delivery is a big, big opportunity," Thompson said, "particularly in areas where you don't have drive-thrus."